You cannot play as the Hulk in the original Marvel: Ultimate Alliance on PS2.
Playable in MUA1 (PS2): Captain America, Spider-Man, Wolverine, Iron Man, Thor, Luke Cage, Ms. Marvel, Deadpool, Ghost Rider, Blade, Daredevil, Silver Surfer, Black Panther, Dr. Strange, Nick Fury, plus unlockables (Colossus, Moon Knight, etc.).
If you want to smash as Hulk on PS2, play Marvel: Ultimate Alliance 2 or The Incredible Hulk: Ultimate Destruction (standalone, excellent).